The World is Flat: A Brief History of the The World is Flat: A Brief History of the Twenty-first CenturyTwenty-first Century

Thomas Friedman, NY TimesThomas Friedman, NY Times

After the fall of the Berlin Wall, and the economic After the fall of the Berlin Wall, and the economic development in Southeast Asia, there are development in Southeast Asia, there are potentially 3 billion more knowledge workers.potentially 3 billion more knowledge workers.

The cost to transfer information is extremely low.The cost to transfer information is extremely low. New requirements: creativity and innovation.New requirements: creativity and innovation.

My JourneyMy Journey

Using a pre-2000 commercial code in classes Using a pre-2000 commercial code in classes proved to be too hard for students to use it on proved to be too hard for students to use it on their own, and it took too much of my time. So I their own, and it took too much of my time. So I stopped trying to introduce finite element stopped trying to introduce finite element simulations of fluid flow and convective heat simulations of fluid flow and convective heat transfer to chemical engineering students.transfer to chemical engineering students.

pde toolbox - pre-2000pde toolbox - pre-2000 FEMLAB - 2D - 2001FEMLAB - 2D - 2001 Comsol Multiphysics - 3D - 2002Comsol Multiphysics - 3D - 2002

Attractive Features to be IllustratedAttractive Features to be Illustrated GUIGUI Draw domain, internal boundariesDraw domain, internal boundaries Automatic mesh generation and refinementAutomatic mesh generation and refinement Solve equations one at a time, on different meshesSolve equations one at a time, on different meshes Easy to add physicsEasy to add physics Easy to modify parameters, even those dependent Easy to modify parameters, even those dependent

upon the solutionupon the solution Parametric solverParametric solver Post-processing capability to validate the solutionPost-processing capability to validate the solution

How I introduce students to Comsol How I introduce students to Comsol MultiphysicsMultiphysics

a) Students solve a problem they have in a) Students solve a problem they have in their textbook - check their work against a their textbook - check their work against a known outcomeknown outcome

b) Students solve a known problem with a b) Students solve a known problem with a slight extension - one that makes the slight extension - one that makes the problem intractable analytically, and that problem intractable analytically, and that uses some of the FEMLAB features - this uses some of the FEMLAB features - this inspires the students to see what is inspires the students to see what is possible.possible.

Important Lesson:Important Lesson:

How to check that your How to check that your results are right!results are right!

Beginning problemsBeginning problems

a) Flow in a pipe b) Heat transfer in 2D

u u0 1

rR2

Solve for fully developed flow in a pipe, with this inlet boundary condition:

and compare with the Hagen-Poiseuille law in your textbook.

Problem has a singularity at one corner.

Project FormulationProject Formulation

Goal oriented, sometimes a model problem, solved Goal oriented, sometimes a model problem, solved in 10 week quarterin 10 week quarter

Organized in 3-5 steps of increasing complexityOrganized in 3-5 steps of increasing complexity Meet weekly, but I’m hands-offMeet weekly, but I’m hands-off After 6 weeks, students are panickingAfter 6 weeks, students are panicking I reassure themI reassure them In weeks 7-8 they begin to get results and they are In weeks 7-8 they begin to get results and they are

inspired - beautiful pictures, show my friends, Wow!, inspired - beautiful pictures, show my friends, Wow!, this is more than my textbooks cover!this is more than my textbooks cover!

Then the innovation starts: What if…Then the innovation starts: What if… More complicated project goals the next quarter.More complicated project goals the next quarter.

My Journey began with pdetool in My Journey began with pdetool in MATLABMATLAB

Solved Poisson’s equation in 2D

2u fAllowed one to adjust coefficients draw the domain (irregular), mesh automatically, refine the mesh on command, solve the problem, and plot the solution and its derivatives.

Ch. E. 475 - Tutorial for using Matlab/PDE Toolbox to solve elliptic boundary value problems

Open Matlab and give the command pdetool. (This only works if one has the professional version with pde toolbox. This is installed in BNS 125.)

Draw click on the square icon and draw a rectanglefor the inner rectangle, do againto make a hole, use R1 – R2double click on the object to set exact dimensions

boundary mode - choose ∂W iconclick on one boundaryor shift click on all boundary segments with the same boundary conditiondouble click on the last one, and set the boundary condition

Mesh click once on triangle iconclick on divided triangle icon to refine the mesh

Pde choose specification - to check the differential equation= click on = to solve the problemPlot set parameters to choose the type of plot

• You can go back and refine the mesh (click the more refined mesh symbol) and resolve the problem. This gives you an indication of the accuracy of the solution.• If you want detailed information about the solution, you must save the solution to the MATLAB command workspace (it is called u), and save the element information (it is called p e t). • Save your work frequently!

Someone did!Someone did!In March, 2001, Suwimol Kunaritipol, a junior Thai exchange student, asked me if she could do an undergraduate research project with me. I had not had much success with undergraduates, due to difficulty in getting a program to run correctly. But, I said, Comsol has just come out with a new program that will solve the Navier-Stokes equations in 2D. It won’t be ready until half the quarter is over, but you can learn on pdetool until then. She accepted, and later in the quarter she came back with results and taught me something! That was when I decided to do more undergraduate projects.

Wouldn’t it be nice if someone did that for the Navier-Stokes equation?

What did she teach me?What did she teach me?

In laminar flow, the pressure drop going around the bend depends only on the pathlength along the center.

Pressure drop in orificePressure drop in orificeElissa Jacobsen and Febe KusmantoElissa Jacobsen and Febe Kusmanto

Orifice diameters as small as 8 microns

Hasegawa, et al., Physics of Fluids,1997 says: Hasegawa, et al., Physics of Fluids,1997 says: ‘this data cannot be predicted using classical ‘this data cannot be predicted using classical

fluid mechanics’fluid mechanics’

100 101 102 103100

101

102

Re

K

Hasegawa, et al. data (1997)

L/D = 0.092L/D = 0.28 L/D = 0.75 L/D = 1.14 numerical

If continuum mechanics does not hold in orifice of 8 microns, how small is small?

100 101 102 103100

101

102

Re

K

Compare Theory to Experiment

L/D = 0.092 L/D = 0.28 L/D = 0.75 L/D = 1.14 num. L/D = 0.092num. L/D = 0.28 num. L/D = 0.75 num. L/D = 1.14

Dagan, et al., J. Fluid Mechanics, 1982, solved the Stokes problem analytically (straight lines). Our finite element simulations for Reynolds number = 0 agree with their solutions. The rest of the curve is numerical, solved for a range of parameters using the parametric solver with Re = 10^x, x=0:0.1:3.

Continuum mechanics can in fact explain data in devices as small as 8 microns.

Pressure Profile at Re = 0 and 316Pressure Profile at Re = 0 and 316

Additional insights using Additional insights using Comsol MultiphysicsComsol Multiphysics

Does the temperature rise enough to Does the temperature rise enough to cause the viscosity to change?cause the viscosity to change?

Solve the energy equation, too, with the Solve the energy equation, too, with the viscous dissipation included using viscous dissipation included using FEMLAB’s ability to put in equations.FEMLAB’s ability to put in equations.

Found the temperature rise was less than Found the temperature rise was less than one degree for an adiabatic channel.one degree for an adiabatic channel.

Work done with Yuli TanWork done with Yuli Tan

That fall, Marlina Lukman and Albert That fall, Marlina Lukman and Albert Witarsa, from Indonesia, began a series Witarsa, from Indonesia, began a series

of projectsof projectsPressure drop in contractions, depend upon geometry and flow rate. Correlations exist for turbulent flow, but not for laminar flow.

Mixing in microfluidic devices

Mixing in the Dow reactor, Zach TyreeMixing in the Dow reactor, Zach Tyree

Entrance of Liquid A

Entrance of Liquid BExit

Need geometry and flow rates, viscosity, but density is not very important at low Re.

Relatively easy at low Reynolds numbers.

Good mixing won’t occur in laminar Good mixing won’t occur in laminar flow.flow.

The concentration distribution at the exit is very different from the velocity distribution and is quite irregular.

Product concentration Axial velocity

Our model became one of the iconsOur model became one of the icons

You see this icon in the Chemical Engineering module.

Serpentine mixer is used to create Serpentine mixer is used to create good mixing in laminar flow in a good mixing in laminar flow in a short distance. Work with Chris short distance. Work with Chris

Niels and Prof. Albert FolchNiels and Prof. Albert Folch

Serpentine mixer, Zach TyreeSerpentine mixer, Zach Tyree

Used Comsol Multiphysics’ ability to solve the convective diffusion equation after the Navier-Stokes equation is solved, and on a different mesh, needed for Peclet number = 2200, 280,000 dof

Comparison with experimentComparison with experiment

Internal view of velocity and Internal view of velocity and concentration - post processing concentration - post processing

leads to insightleads to insight

Convective Instability, Michael HarrisonConvective Instability, Michael Harrison

Thermal diffusion, Pawel DrapalaThermal diffusion, Pawel Drapala

Mimicking the concentration of DNA by thermal gradients, experiments by Braun and Libchaber, Phys. Rev. Lett., 2002

Flow in an Aluminum CellFlow in an Aluminum CellZudtky WisecarverZudtky Wisecarver

Use Comsol Multiphysics’ ability to draw the geometry, and solve the problem in 3D.

Chemical Spills - Megan McMauleyChemical Spills - Megan McMauley

Height z = 8.72 mz+

Turbulent theory/FEMLAB = Nearly constant velocity profile

Flow past flat plate = variable velocity profile

Height δ = 3.8 m

:10z zu

:10z zu ln5.21.5

:450 z

:45z

zm 4.0

2/12

3

0067.01

00090.0

z

zm

zSc

zScxu m

11

EquationsEquations

Governing equation Governing equation Convection and diffusionConvection and diffusion Steady-stateSteady-state

Eddy-diffusivityEddy-diffusivity

uu++ is x-velocity is x-velocity

Used Comsol Multiphysics to validate a published solution and determine that the evaporation rate predicted is highly dependent upon the assumption of flow geometry.

Mixing of polymer solution to make Mixing of polymer solution to make sludge flocculatesludge flocculate

Problem posed by Sharpe Mixers and the Renton Wastewater Treatment Plant: Is it in laminar flow?

A polymer solution is added to digested sludge in A polymer solution is added to digested sludge in order to cause it to flocculate. The sludge is then order to cause it to flocculate. The sludge is then sent to a centrifuge to separate the water from the sent to a centrifuge to separate the water from the sludge, which is used for fertilizer. This project sludge, which is used for fertilizer. This project began as a study of the incomplete mixing of the began as a study of the incomplete mixing of the polymer. The goal of the Renton Wastewater polymer. The goal of the Renton Wastewater Treatment Plant is to reduce the cost of the polymer Treatment Plant is to reduce the cost of the polymer by achieving good mixing with less polymer.by achieving good mixing with less polymer.

Designed a project for 11 students

• measure the viscosity as a function of concentration

• solve the flow problem with two pipes leading to one pipe

• use the static mixer in the Comsol library

• make the static mixer rotate

Students went through the standard introduction to Comsol Multiphysics and then began work.

ViscosityViscosity75% Polymer Solution Over-Mixed

y = -0.806x + 3.3675

R2 = 0.9952

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

-1.5 -1 -0.5 0 0.5 1 1.5

Log Shear RateL

og

Vis

cosi

ty

SolutionSolution Power law indexPower law index

PolymerPolymer 0.3190.319

SludgeSludge 0.2510.251

Over-MixedOver-Mixed 0.0550.055

Mixing with power law fluidMixing with power law fluid

I was willing to settle for a Newtonian solution; students wanted a full power-law model and succeeded.

Little mixing, even in 8 feetLittle mixing, even in 8 feet

Discovered that the flow is laminarDiscovered that the flow is laminar

A longer pipe won’t help much. This was news to the polymer manufacturer.

Used Comsol Multiphysics Used Comsol Multiphysics with patents in graduate fluid with patents in graduate fluid

mechanics class - 2002mechanics class - 2002

Optical DetectionOptical Detection (Janine Buseman-Williams, Jon Ladd, Jamie Wilson)(Janine Buseman-Williams, Jon Ladd, Jamie Wilson)

•Analytes pass through column and are carried along optical detection pathlength •Beer’s Law: A = * b * C•Extended Pathlength of up to 1 mm

Optically Transparent

Optically Transparent

Velocity Profile and Velocity Profile and Device Geometry Device Geometry

FEMLAB Choices: DiffusivityFEMLAB Choices: Diffusivity

The students also made movies of the slug of material passing through the device.

Comsol multiphysics made it easy for students to innovate - they did much more than was required.

The next year the class size doubled.

Medical devices on a chipMedical devices on a chip Interdiffusion-based enzyme inhibition Interdiffusion-based enzyme inhibition

assayassay Dissolution from cavity as a way of Dissolution from cavity as a way of

delivering drugs on demanddelivering drugs on demand

Elena Garcia/Prof. Paul YagerElena Garcia/Prof. Paul Yager

Surface binding of antigen Surface binding of antigen Jennifer Foley/ Prof. Paul YagerJennifer Foley/ Prof. Paul Yager

1)1) Solve N-SSolve N-SVelocity profileVelocity profile

~10,000 elements~10,000 elements

~200 seconds to solve~200 seconds to solve

2) Solve C-D/Surface Rxn

~13,000 elements

~45 minutes to solve

Antibody binding region

Surface EquationsSurface Equations

Weak Boundary ModeWeak Boundary Mode

Theta (# of available binding sites/area)

C – bulk antigen concentration

Cs – surface bound antigen concentration

Concentration further depleted with Concentration further depleted with lower flow ratelower flow rate

MAX 1.01

OUTLET WALL

PLANE

OF SYMMETRY

AB PATCH

Heat Transfer to FerrofluidHeat Transfer to FerrofluidSuzanne SnyderSuzanne Snyder

Comsol Multiphysics made it possible to easily solve using a user-specified body force, and do it easily in 3D.

Introduction to Chemical Introduction to Chemical Engineering ComputingEngineering Computing

Philosophy - students can be good Philosophy - students can be good chemical engineers without understanding chemical engineers without understanding the details of the numerical analysis.the details of the numerical analysis.

By using modern programs with good By using modern programs with good GUIs, the most important thing is to check GUIs, the most important thing is to check your results.your results.

Instead of teaching a small fraction of the Instead of teaching a small fraction of the class numerical methods, I now teach all class numerical methods, I now teach all the class to use the computer wisely.the class to use the computer wisely.

ProgramsPrograms

Microsoft Excel ®Microsoft Excel ® MATLAB®MATLAB® Aspen Plus ®Aspen Plus ® FEMLAB ®FEMLAB ®

Available, Dec., 2005

Chemical reactor models with radial dispersion, Chemical reactor models with radial dispersion, axial dispersionaxial dispersion

Catalytic reaction and diffusionCatalytic reaction and diffusion One-dimensional transport problems in fluid One-dimensional transport problems in fluid

mechanics, heat and mass transfermechanics, heat and mass transfer Newtonian and non-NewtonianNewtonian and non-Newtonian Pipe flow, steady and start-upPipe flow, steady and start-up adsorbtionadsorbtion

Two- and three-dimensional transport problems Two- and three-dimensional transport problems in fluid mechanics, heat and mass transferin fluid mechanics, heat and mass transfer Entry flowEntry flow Laminar and turbulentLaminar and turbulent Microfludics, high Peclet numberMicrofludics, high Peclet number Temperature effects (viscous dissipation)Temperature effects (viscous dissipation) Proper boundary conditionsProper boundary conditions

ConclusionsConclusions

Comsol Multiphysics is your problem-solving partner.

It provides simulation for the flat world generation.

It helped me grow my vision, one student at a time.

It provides and promotes:

Motivation - Responsibility - Innovation and Creativity.